# Direct-product-closed subgroup property

This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
View a complete list of subgroup metaproperties
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

### Definition with symbols

A subgroup property $p$ is said to be direct-product-closed if whenever $H_1 \le G_1$ satisfies $p$, and $H_2 \le G_2$ satisfies $p$, then $H_1 \times H_2$ satisfies $p$ as a subgroup of $G_1 \times G_2$.